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Full Description
This book presents the theory of plates and shells on the basis of the three-dimensional parent theory. The authors explore the thinness of the structure to represent the mechanics of the actual thin three-dimensional body under consideration by a more tractable two-dimensional theory associated with an interior surface. In this way, the relatively complex three-dimensional continuum mechanics of the thin body is replaced by a far more tractable two-dimensional theory. To ensure that the resulting model is predictive, it is necessary to compensate for this 'dimension reduction' by assigning additional kinematical and dynamical descriptors to the surface whose deformations are modelled by the simpler two-dimensional theory. The authors avoid the various ad hoc assumptions made in the historical development of the subject, most notably the classical Kirchhoff-Love hypothesis requiring that material lines initially normal to the shell surface remain so after deformation. Instead, suchconditions, when appropriate, are here derived rather than postulated.
Contents
Chapter 1. Tensor Analysis in Euclidean Space Using Curvilinear Coordinates.- Chapter 2. Local Geometry of Deformation.- Chapter 3. Hyperelastic Solids: Purely Mechanical Theory.- Chapter 4. Linearly elastic plates.- Chapter 5. Linear Shell Theory.- Chapter 6. Nonlinear equations for plates and shells.- Chapter 7. Buckling of elastic plates.- Chapter 8. Saint-Venant Problem for general cylindrical shells.
